Nitrogen Doped and Vacancy Dominated Silicon Ingot and Thermally Treated Wafer Formed Therefrom Having Radially Uniformly Distributed Oxygen Precipitation Density and Size

ABSTRACT

Nitrogen-doped CZ silicon crystal ingots and wafers sliced therefrom are disclosed that provide for post epitaxial thermally treated wafers having oxygen precipitate density and size that are substantially uniformly distributed radially and exhibit the lack of a significant edge effect. Methods for producing such CZ silicon crystal ingots are also provided by controlling the pull rate from molten silicon, the temperature gradient and the nitrogen concentration. Methods for simulating the radial bulk micro defect size distribution, radial bulk micro defect density distribution and oxygen precipitation density distribution of post epitaxial thermally treated wafers sliced from nitrogen-doped CZ silicon crystals are also provided.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No.62/031,203 filed Jul. 31, 2014.

BACKGROUND

The field of the disclosure relates generally to semiconductor gradesingle crystal silicon which is used in the manufacture of electroniccomponents and methods for preparation thereof. More particularly, thepresent disclosure relates to vacancy dominated single crystal siliconingots and wafers sliced therefrom that are doped with nitrogen andprovide for thermally treated silicon wafers having oxygen precipitatedensity and size that are uniformly distributed radially and exhibit thelack of a significant edge effect.

Single crystal silicon, from which a single crystal silicon wafer may beobtained, is commonly prepared by the so-called Czochralski (“CZ”)method. In this method, polycrystalline silicon (“polysilicon”) ischarged to a crucible and melted, a seed crystal is brought into contactwith the molten silicon, and a single crystal is grown by slowextraction. After formation of a neck is complete, the diameter of thecrystal is enlarged by decreasing the pull rate and/or the melttemperature until the desired or target diameter is reached. Thecylindrical main body of the crystal having an approximately constantdiameter is then grown by controlling the pull rate and the melttemperature while compensating for the decreasing melt level. Near theend of the growth process, but before the crucible is emptied of moltensilicon, the crystal diameter is typically reduced gradually to form anend-cone. Typically, the end-cone is formed by increasing the crystalpull rate and heat supplied to the crucible. When the diameter becomessmall enough, the crystal is then separated from the melt.

It is recognized that a number of defects in single crystal silicon formin the crystal growth chamber as the crystal cools after solidification.Such defects arise, in part, due to the presence of an excess (i.e., aconcentration above the solubility limit) of intrinsic point defects,which are known as crystal lattice vacancies (“V”) and siliconself-interstitials (“I”). The type and initial concentration of theintrinsic point defects are determined at the time of solidificationand, if these concentrations reach a level of critical super saturationin the system and the mobility of the point defects is sufficientlyhigh, a reaction, or an agglomeration event, will likely occur.Agglomerated intrinsic point defects in silicon, including bulk microdefects (“BMD”) such as oxygen precipitates, can impact the yieldpotential of the material in the production of complex and highlyintegrated circuits.

Agglomerated vacancy-type defects include such observable crystaldefects as D-defects, Flow Pattern Defects (FPDs), Crystal OriginatedParticle (COP) Defects, crystal originated Light Point Defects (LPDs),as well as certain classes of bulk defects observed by infrared lightscattering techniques such as Scanning Infrared Microscopy and LaserScanning Tomography. Oxygen precipitates are generated from oxygenprecipitation nuclei that are formed during the growth of the ingot.More particularly, oxygen precipitation nuclei are necessary for theformation of oxygen precipitates during subsequent thermal processingassociated with electronic device fabrication. The oxygen precipitatesact as gettering sites for capturing metallic impurities in the bulk ofthe wafer and away from the surface. Without the ability to gettermetallic impurities, the electronic properties of the wafer may benegatively impacted; for example, the wafer may have a decreasedminority carrier lifetime, current leakage at p-n junctions, dielectricconstant discontinuity and reduced breakdown strength. In semiconductordevice fabrication, there are increasing demands for adequate and robustgettering capability from oxygen precipitation in the bulk of siliconwafers while avoiding yield degradation related to oxygen precipitationat the same time.

Nitrogen-doped silicon crystals are being produced and used in variousapplications, largely due to the nitrogen-induced decrease in void sizedistributions. It is believed that, acting through vacancy trapping,nitrogen affects point defect formation in the vacancy region of thecrystal, essentially shifts void formation to lower temperatures,increases the void density, and decreases the void size. Because of thetrapping effect of vacancies in nitrogen doped crystals, oxygenprecipitations are formed at higher density and larger sizes than innon-nitrogen doped crystals. To achieve satisfactory BMD capabilitieswithout generating defects in polished, Epi, and annealed wafers, aswell as in customers' applications, the wafers preferably exhibitsubstantially uniform radial density and size distributions of oxygenprecipitations after thermal treatment. In some advanced semiconductordevice fabrication, such larger precipitations, at higher density, arenot substantially uniformly distributed, and can be problematic forvarious reasons. In particular, wafers sliced from nitrogen dopedsilicon crystals typically exhibit an increase in the BMD size anddensity profiles at the edge portions of the wafer after thermaltreatment. Without being bound to any particular theory, it is believedthat nitrogen bonds strongly with vacancies, and lower nitrogenconcentration will amount to more free vacancies which, in turn, favorformation of voids. As a result, oxygen precipitates become smaller andthe density is reduced in the interior regions of the crystal ascompared to the edge of the crystal where, due to the presence of thesurface-induced effects, the oxygen precipitate size and density trendupward in what is termed the “edge effect.”

In edge effect, BMD size and density profiles characteristically trendupward at the edge portions of prior art wafer sliced fromnitrogen-doped CZ silicon crystals. As shown in FIGS. 1 and 2, analysisof two prior art 300 mm diameter wafers sliced from nitrogen-doped CZsilicon crystals grown at a pull rate of about 0.78 mm/minute at atemperature differential of about 50° C./cm are depicted. The crystalwas annealed at 1130° C. for Epi and with a 2-step thermal cycle for thepurpose of characterizing the precipitations, with the first step at780° C. for 3 hours and the second step at 1000° C. for 16 hours. Theoxygen concentration was in the range of from 10 to 11 ppma, and thenitrogen concentration was in the range of from 3*10¹³ to 2*10¹⁴ atomsper cm³. As shown in FIGS. 1 and 2, analysis of the two wafers show thatthe BMD size and density increased about 300% within 5 millimetersradially at the edge of the wafers.

One approach to dealing with the problem of agglomerated intrinsic pointdefects includes growing the silicon crystal ingot at a high rate in anattempt to cause the ingot to be “vacancy dominated” (i.e., siliconwherein vacancies are the predominant intrinsic point defect) and thenepitaxially depositing a thin crystalline layer of silicon on thesurface of the vacancy dominated single crystal silicon wafer, therebyeffectively filling or covering the agglomerated vacancy defects. Theepitaxial deposition process typically involves a chemical vapordeposition process wherein a single crystal silicon wafer is rapidlyheated to a temperature of about 1150° C. while a gaseous siliconcompound is passed over the wafer surface to deposit a silicon layerthat is substantially free of agglomerated vacancy defects. Theepitaxial deposition process typically annihilates oxygen precipitationnuclei formed during the growth of the ingot. One method for dealingwith the problem of annihilating oxygen precipitation nuclei duringepitaxial deposition is a lengthy thermal annealing process (e.g., about4 hours at about 800° C. followed by 10 hours at about 1000° C.) tostabilize the oxygen precipitation nuclei against the rapid thermalepitaxial deposition process. Problematically, this method decreasesthroughput and significantly increases the cost of manufacturing thesilicon wafers.

Kulkarni (U.S. Pat. No. 8,216,362) addressed the issue of lateralsurface induced agglomeration of vacancies and oxygen clustering in CZsilicon crystal. However, the disclosed method focuses on the control ofthe lateral incorporation of vacancies at pull rates close to thecritical pull rate according to the theory of Voronkov for transitionfrom an interstitial dominated regime to a vacancy dominated regime.Thus, the pull rates disclosed by Kulkarni are relatively low. Accordingto Voronkov's model, or theory, the temperature field in the vicinity ofthe melt/crystal interface drives the recombination of the point defectsproviding driving forces for their diffusion from the melt/crystalinterface—where they exist at their respective equilibriumconcentrations—into the crystal bulk. The interplay between thetransport of the point defects, both by the diffusion and theconvection, and their recombination establishes the point defectconcentration beyond a short distance away from the interface, termedthe recombination length. Typically, the difference between the vacancyconcentration and the interstitial concentration beyond therecombination length, termed the excess point defect concentration,remains essentially fixed away from the lateral surface of the crystal.In a rapidly pulled crystal, the spatial redistribution of the pointdefects by their diffusion beyond the recombination length is generallynot important—with the exception of a region close to the lateralsurface of the crystal that acts as a sink or a source of the pointdefects. Therefore, if the excess point defect concentration beyond therecombination length is positive, vacancies remain in excess, andagglomerate to form D-defects (vacancy agglomerates identified asoctahedral voids) at lower temperatures. If the excess point defectconcentration is negative, interstitials remain the dominant pointdefects, and agglomerate to form A-defects (dislocation loops, termed Aswirl defect) and B-defects (globular interstitial clusters, termed Bswirl defect). If the excess point defect concentration is below somedetection threshold, no detectable microdefects are formed. Thus,typically, the type of grown-in microdefects is determined. Hence,typically, the type of grown-in microdefects is determined simply by theexcess point defect concentration established beyond the recombinationlength. The process of establishing the excess point defectconcentration is termed the initial incorporation and the dominant pointdefect species is termed the incorporated dominant point defect. Thetype of the incorporated point defects is determined by the ratio of thecrystal pull-rate (v) to the magnitude of the axial temperature gradientin the vicinity of the interface (G). At a higher v/G, the convection ofthe point defects dominates their diffusion, and vacancies remain theincorporated dominant point defects, as the vacancy concentration at theinterface is higher than the interstitial concentration. At a lower v/G,the diffusion dominates the convection, allowing the incorporation ofthe fast diffusing interstitials as the dominant point points. At a v/Gclose to its critical value, both the point defects are incorporated invery low and comparable concentrations, mutually annihilating each otherand thus suppressing the potential formation of any microdefects atlower temperatures. The observed spatial microdefect distribution can betypically explained by the variation of v/G, caused by a radialnon-uniformity of G and by an axial variation of v. One feature of theradial microdefect distribution is that the oxide particles form throughthe interaction of oxygen with vacancies in the regions of relativelylower incorporated vacancy concentration at a small range of v/Gmarginally above the critical v/G. These particles form a narrow spatialband that can be revealed by thermal oxidation as the OSF(oxidation-induced stacking faults) ring.

Kulkarni further suggests that the lateral incorporation effect may becontrolled by interface shape manipulation and changes in cooling rates.In particular, a G_(corrected) value is calculated representing arevised G value that takes into account the deviation in the interfaceshape from a flat surface. Further, as the cooling rate of a given ingotsegment increase, the number density of agglomerated defects thereinincreases, while the size of the agglomerated defects decreases. If thecooling rate for the ingot segment is sufficiently high, the formationof agglomerated defects may essentially be avoided. Problematically,either the interface shape manipulation or the cooling rate change arenot sufficient to achieve the desired (i) radial uniformity of vacancyradius and density, (ii) radial uniformity of BMD diameter and densityas a function of crystal radial location and (iii) substantial absenceof an edge effect.

As new technology in device fabrication emerges and the size andstructure of devices continue to become smaller and more complex, it isdesired to obtain radial uniformity of BMD in controlled size anddensity in epitaxial wafers. A need therefore exists for nitrogen dopedsilicon wafers exhibiting a radial uniformly distributed oxygenprecipitate density and size and with control of the edge band of oxygenprecipitates.

BRIEF SUMMARY

Briefly, the present disclosure is directed to a method of producing anitrogen-doped CZ silicon crystal ingot. The method comprises pullingthe silicon crystal ingot from molten silicon at a pull rate of fromabout 0.85 mm per minute to about 1.5 mm per minute, wherein the siliconcrystal ingot has a surface temperature gradient of from about 10° K percm to about 35° K per cm, and wherein the silicon crystal ingot has anitrogen concentration of from about 1*10¹³ atoms per cm³ to about1*10¹⁵ atoms per cm³ thereby forming the nitrogen-doped CZ siliconcrystal ingot.

The present disclosure is further directed to a nitrogen-doped CZsilicon crystal ingot. The ingot has a diameter of from about 150 mm toabout 450 mm and has a nitrogen concentration of from about 1*10¹³nitrogen atoms per cm³ to about 1*10¹⁵ nitrogen atoms per cm³. A wafersliced from the silicon crystal ingot and thermally treated at 780° C.for 3 hours and then at 1000° C. for 16 hours is characterized by anincrease in radial bulk micro defect size in a region extending from thecenter of said wafer to the edge of said wafer of less than 20%.

The present disclosure is yet further directed to a nitrogen-doped CZsilicon crystal ingot. The ingot has a diameter of from about 150 mm toabout 450 mm and comprises from about 1*10¹³ nitrogen atoms per cm³ toabout 1*10¹⁵ nitrogen atoms per cm³. A wafer sliced from the siliconcrystal ingot and thermally treated at 780° C. for 3 hours and then at1000° C. for 16 hours is characterized by an increase in radial bulkmicro defect density in a region extending from the center of said waferto the edge of said wafer of less than 200%.

The present disclosure is still further directed to a nitrogen-doped CZsilicon crystal ingot. The ingot has a diameter of from about 150 mm toabout 450 mm and comprises from about 1*10¹³ nitrogen atoms per cm³ toabout 1*10¹⁵ nitrogen atoms per cm³. A wafer sliced from the siliconcrystal ingot and thermally treated at 780° C. for 3 hours and then at1000° C. for 16 hours has an edge band in a region extending from about1000 μm to the edge of said wafer and the edge of said wafer, the edgeband comprising oxygen precipitates having an average diameter of fromabout 30 nm to about 100 nm and an oxygen precipitation density of fromabout 1*10⁸ atoms per cm³ to about 1*10¹⁰ atoms per cm³.

In some particular embodiments of the present disclosure, a polished andepitaxial wafer is made from any of the above-noted nitrogen-doped CZsilicon crystal ingots. The wafer is a single crystal CZ silicon wafersliced from the CZ silicon single crystal ingot and comprises a frontsurface, a back surface, a central plane between the front and backsurfaces, a circumferential edge joining the front and back surface, acentral axis perpendicular to the central plane, and a bulk layer whichcomprises the region of the wafer between the central plane and frontsurface.

In other aspects of the present disclosure, a method is provided forsimulating the radial bulk micro defect size distribution, radial bulkmicro defect density distribution and oxygen precipitation densitydistribution in wafers sliced from nitrogen-doped CZ silicon crystalsand thermally treated at 780° C. for 3 hours and then at 1000° C. for 16hours. The method is implemented by a computing device including aprocessor coupled to a memory, the method comprises completing at leastone iteration of a simulation scheme comprising: (1) receiving, by thecomputing device, values for at least (i) a CZ silicon crystal diameter,(ii) a CZ silicon crystal pull rate or a CZ silicon crystal pull raterange, (iii) a CZ silicon crystal nitrogen concentration or a CZ siliconcrystal nitrogen concentration range and (iv) a CZ silicon crystalsurface temperature gradient or a CZ silicon crystal surface temperaturegradient range, and simulating, by the computing device, a thermallytreated wafer radial bulk micro defect size distribution in a regionextending from the center of said wafer to the edge of said wafer basedon the received values; (2) receiving, by the computing device, valuesfor at least (i) the CZ silicon crystal diameter, (ii) the CZ siliconcrystal pull rate or the CZ silicon crystal pull rate range and (iii)the CZ silicon crystal nitrogen concentration or the CZ silicon crystalnitrogen concentration range, and simulating, by the computing device, athermally treated wafer radial bulk micro defect density distribution ina region extending from the center of said wafer to the edge of saidwafer based on the received values; and (3) receiving, by the computingdevice, values for at least (i) the CZ silicon crystal diameter, (ii)the CZ silicon crystal pull rate or the CZ silicon crystal pull raterange, (iii) the CZ silicon crystal nitrogen concentration or the CZsilicon crystal nitrogen concentration range and (iv) the CZ siliconcrystal surface temperature gradient or the CZ silicon crystal surfacetemperature gradient range and simulating, by the computing device, athermally treated wafer oxygen precipitation density distribution in aregion extending from the center of said wafer to the edge of saidwafer. The CZ silicon crystal has a diameter of from about 150 mm toabout 450 mm, comprises from about 1*10¹³ nitrogen atoms per cm³ toabout 1*10¹⁵ nitrogen atoms per cm³, and the thermally treated wafer hasan edge band region in a region extending from about 1000 μm to the edgeof said wafer to the edge of said wafer. A combination of CZ siliconcrystal pull rate or CZ silicon crystal pull rate range, CZ siliconcrystal nitrogen concentration or CZ silicon crystal nitrogenconcentration range, and CZ silicon crystal surface temperature gradientor CZ silicon crystal surface temperature gradient range is derived fromthe simulation to provide conditions for preparing a thermally treatedwafer having (i) an increase in radial bulk micro defect sizedistribution in a region extending from the center of said wafer to theedge of said wafer of less than 20% and/or (ii) an increase in radialbulk micro defect density distribution in a region extending from thecenter of said wafer to the edge of said wafer of less than 200%.

In still further aspects of the present disclosure, a method ofcontrolling the edge band of oxygen precipitates in wafers sliced fromnitrogen-doped CZ silicon crystals and thermally treated at 780° C. for3 hours and then at 1000° C. for 16 hours is provided. The method isimplemented by a computing device including a processor coupled to amemory. The method comprises determining, by the computing device, bysimulation, a combination of (i) CZ silicon crystal diameter, (ii) CZsilicon crystal pull rate or CZ silicon crystal pull rate range, (iii)CZ silicon crystal nitrogen concentration or CZ silicon crystal nitrogenconcentration range, and (iv) CZ silicon crystal surface temperaturegradient or CZ silicon crystal surface temperature range that enablesthe preparation of a CZ silicon crystal ingot from molten silicon by theCZ process wherein a thermally treated wafer sliced therefrom and havingan edge band region in a region extending from about 1000 μm to the edgeof said wafer to the edge of said wafer is characterized by oxygenprecipitates having an average diameter of from about 30 nm to about 100nm. The CZ silicon crystal has a diameter of from about 150 mm to about450 mm and the nitrogen concentration in the CZ silicon crystal is fromabout 1*10¹³ atoms per cm³ to about 1*10¹⁵ atoms per cm³. The simulationcomprises at least one iteration of a simulation scheme comprising: (1)receiving, by the computing device, values for at least (i) a CZ siliconcrystal diameter, (ii) a CZ silicon crystal pull rate or a CZ siliconcrystal pull rate range, (iii) a CZ silicon crystal nitrogenconcentration or a CZ silicon crystal nitrogen concentration range and(iv) a CZ silicon crystal surface temperature gradient or a CZ siliconcrystal surface temperature gradient range, and simulating, by thecomputing device, a thermally treated wafer radial bulk micro defectsize distribution in a region extending from the center of said wafer tothe edge of said wafer based on the received values; (2) receiving, bythe computing device, values for at least (i) the CZ silicon crystaldiameter, (ii) the CZ silicon crystal pull rate or the CZ siliconcrystal pull rate range and (iii) the CZ silicon crystal nitrogenconcentration or the CZ silicon crystal nitrogen concentration range,and simulating, by the computing device, a thermally treated waferradial bulk micro defect density distribution in a region extending fromthe center of said wafer to the edge of said wafer based on the receivedvalues; (3) receiving, by the computing device, values for at least (i)the CZ silicon crystal diameter, (ii) the CZ silicon crystal pull rateor the CZ silicon crystal pull rate range, (iii) the CZ silicon crystalnitrogen concentration or the CZ silicon crystal nitrogen concentrationrange and (iv) the CZ silicon crystal surface temperature gradient orthe CZ silicon crystal surface temperature gradient range andsimulating, by the computing device, a thermally treated wafer oxygenprecipitation density distribution in a region extending from the centerof said wafer to the edge of said wafer; and (4) simulating, by thecomputing device, the average size of the thermally treated wafer edgeband oxygen precipitates based on the simulated values for (i) thethermally treated wafer radial bulk micro defect size distribution fromthe center of said wafer to the edge of said wafer, (ii) the thermallytreated wafer radial bulk micro defect density distribution from thecenter of said wafer to the edge of said wafer, and (iii) the thermallytreated wafer density distribution in a region extending from the centerof said wafer to the edge of said wafer, wherein the computing devicepredicts the thermally treated wafer edge band by simulation to compriseoxygen precipitates having an average diameter of from about 30 nm toabout 100 nm. The CZ silicon crystal is pulled from the molten siliconat the simulated values of CZ silicon crystal pull rate or CZ siliconcrystal pull rate range, CZ silicon crystal nitrogen concentration or CZsilicon crystal nitrogen concentration range, and CZ silicon crystalsurface temperature gradient or CZ silicon crystal surface temperaturerange to produce the nitrogen-doped CZ silicon crystal from which thetreated wafers are produced.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph showing the radial BMD size (diameter) distributionfor prior art nitrogen doped 300 mm diameter thermally treated waferssliced from CZ crystal depicting increased BMD size at the crystal edge.

FIG. 2 is a graph showing the radial BMD density profile distributionfor prior art nitrogen doped 300 mm diameter thermally treated waferssliced from CZ crystal depicting increased BMD density at the crystaledge.

FIG. 3 is a graph showing the predicted effect of pull rate on theradius of as-grown crystal clusters as a function of crystal radiallocation across the crystal cross section of a 30 cm diameter CZ siliconcrystal.

FIG. 4 is a graph showing the predicted effect of pull rate on theradius of as-grown voids (vacancy clusters) as a function of crystalradial location across the crystal cross section of a 30 cm diameter CZsilicon crystal.

FIG. 5 is a graph showing the predicted average BMD density as afunction of pull rate for constant high temperature annealing done at1100° C.

FIG. 6 is a graph showing the predicted average BMD density as afunction of pull rate for constant high temperature annealing done at1000° C.

FIG. 7 is a graph showing the predicted effect of nitrogen concentrationon the radii of as-grown oxygen precipitates as a function of crystalradial location across the crystal cross section of a 30 cm diameter CZsilicon crystal.

FIG. 8 is a graph showing the predicted effect of nitrogen concentrationon the radii of as-grown voids as a function of crystal radial locationacross the crystal cross section of a 30 cm diameter CZ silicon crystal.

FIG. 9 is a graph showing the predicted average BMD density as afunction of nitrogen concentration for constant high temperatureannealing done at 1100° C.

FIG. 10 is a graph showing the predicted average BMD density as afunction of nitrogen concentration for constant high temperatureannealing done at 1100° C.

FIG. 11 is a graph showing the predicted effect of crystal surfacetemperature gradient on the radii of as-grown oxygen precipitatesplotted as a function of radial location across the crystal crosssection of a 30 cm diameter CZ silicon crystal.

FIG. 12 is a graph showing the predicted effect of crystal surfacetemperature gradient on the radii of as-grown voids plotted as afunction of radial location across the crystal cross section of a 30 cmdiameter CZ silicon crystal.

FIG. 13 is a graph showing the predicted average BMD density as afunction of crystal surface temperature gradient for constant hightemperature annealing done at 1100° C.

FIG. 14 is a graph showing the predicted average BMD density as afunction of crystal surface temperature gradient for constant hightemperature annealing done at 1000° C.

FIG. 15 is a graph showing the predicted radii of as-grown oxygenprecipitates as a function of radial location across a crystalcross-section for nitrogen doped 300 mm diameter CZ crystals of thepresent disclosure (combinations 1-4) and for a prior art nitrogen doped300 mm diameter CZ crystal (conventional (#0)).

FIG. 16 is a graph showing the predicted radii of as-grown voids as afunction of radial location across a crystal cross-section for nitrogendoped 300 mm diameter CZ crystals of the present disclosure(combinations 1-4) and for a prior art nitrogen doped 300 mm diameter CZcrystal (conventional (#0)).

FIG. 17 is a graph showing the predicted average BMD density as afunction of crystal surface temperature gradient for constant hightemperature annealing done at 1100° C. for nitrogen doped 300 mmdiameter CZ crystals of the present disclosure and for a prior art anitrogen doped 300 mm diameter CZ crystal.

FIG. 18 is a graph showing the predicted average BMD density as afunction of crystal surface temperature gradient for constant hightemperature annealing done at 1000° C. for nitrogen doped 300 mmdiameter CZ crystals of the present disclosure and for a prior art anitrogen doped 300 mm diameter CZ crystal.

FIG. 19 is a graph showing the predicted oxide precipitate densityacross the depth of a wafer without nitrogen doping at times 0.024 hour,0.23 hour, 0.51 hour and 1 hour for annealing at 800° C. with an initialtotal vacancy concentration (C_(vt)) of 6*10¹² numbers per cm³ and anoxygen concentration (C_(O)) of 8*10¹⁷ atoms per cm³.

FIG. 20 is a graph showing the predicted total vacancy concentration innumber per cm³ across the depth of a wafer without nitrogen doping attimes 0.024 hour, 0.23 hour, 0.51 hour and 1 hour for annealing at 800°C. with an initial total vacancy concentration (C_(vt)) of 6*10¹²numbers per cm³ and an oxygen concentration (C_(O)) of 8*10¹⁷ atoms percm³.

FIG. 21 is a graph showing the average BMD size (diameter) as a functionof radial location across a crystal cross-section for nitrogen doped 300mm diameter thermally treated wafers sliced from CZ crystals of thepresent disclosure.

FIG. 22 is a graph showing the BMD density profile as a function ofradial location across a crystal cross-section for nitrogen doped 300 mmthermally treated wafers sliced from diameter CZ crystals of the presentdisclosure.

FIG. 23 is a flow chart for one method of the present disclosure forsimulating and evaluating edge band bulk micro defect size and density.

DETAILED DESCRIPTION

In accordance with the present disclosure, a nitrogen-doped CZ singlecrystal silicon ingot and wafer produced therefrom is provided, theingot is characterized by substantial radial uniformity of vacancyradius and density as a function of crystal radial location across acrystal cross section, and a thermally treated wafer sliced therefrom ischaracterized by substantial radial uniformity of BMD diameter anddensity as a function of crystal radial location across a crystal crosssection, wherein the ingot and wafer exhibit the substantial absence ofan edge effect.

In further accordance with the present disclosure, a method is providedfor preparing a nitrogen-doped CZ single crystal silicon ingotcharacterized by substantial radial uniformity of vacancy radius anddensity as a function of crystal radial location across a crystal crosssection and providing for a thermally treated wafer sliced therefromcharacterized by substantial radial uniformity of BMD diameter anddensity as a function of crystal radial location across a crystal crosssection, wherein the wafer exhibits the substantial absence of an edgeeffect, the method comprising controlling pull rate, surface temperaturegradient and nitrogen concentration in the preparation of a singlecrystal ingot from molten silicon in a CZ process.

In yet further accordance with the present disclosure, a method tosimulate the agglomeration of vacancies in as grown nitrogen-doped CZsingle crystal silicon ingots and oxygen clustering in wafers slicedtherefrom after various thermal treatments is provided, the simulationemploying algorithms that predict the BMD size and density distributionand the edge band characteristics for a given diameter based on acombination variables including pull rate, nitrogen dopingconcentration, and crystal surface temperature gradient.

In any of the various aspects of the present disclosure, selection of acombination of (i) CZ silicon crystal ingot or wafer diameter selectedfrom about 150 mm to about 450 mm, (ii) a nitrogen concentration withinthe range of from about 1*10¹³ to about 1*10¹⁵, (iii) a pull rate rangesubset within a range of from about 0.4 mm per minute to about 1.5 mmper minute, and (iv) a surface temperature gradient subset range withina range of from about 10° K per cm to about 50° K per cm at an averagecrystal surface temperature of from about 1300° C. to about 1415° C.provide for doped nitrogen wafers characterized, for any given diameter,by one or more of (i) an increase in radial bulk micro defect size in aregion extending from the center of said wafer to the edge of said waferof less than 20%, (ii) an increase in radial bulk micro defect densityin a region extending from the center of said wafer to the edge of saidwafer of less than 200% and (iii) the essential absence of an edge bandeffect.

Silicon crystal ingots and wafers of the present disclosure have adiameter of at least about 150 mm, at least about 200 mm, at least about250 mm, or at least about 300 mm, such as about 150 mm, 200 mm, 250 mm,300 mm, 350 mm, 400 mm or 450 mm. In some aspects, the diameter is about300 mm. It should be noted that while silicon ingots are generallyreferred to as having a diameter of 150 mm, 200 mm, 250 mm, 300 mm orgreater than 300 mm, such as 350 mm, 400 mm or 450 mm, the precisediameter may vary somewhat along the axial length due to minorvariations in the process or may vary intentionally in order to grow aningot capable of producing similarly sized wafers. For example, as isknown to those skilled in the art, a 300 mm diameter ingot or wafer mayoptionally be prepared from an ingot or wafer of a diameter in excess of300 mm, such as for instance 310 mm or 320 mm or more and subsequentlyhave a portion removed from the peripheral portion of the ingot or waferany process known in the art, such as grinding, to reduce the diameterof the ingot or wafer.

The thermally treated wafers sliced from the ingots of the presentdisclosure are characterized by an increase in BMD size in a regionextending from the center of the wafer to the edge of the wafer of lessthan 20% or by an increase in bulk micro defect size in a regionextending from about 10 mm to the edge of the wafer to the edge of thewafer of less than 15%. The wafers are further characterized by anincrease in bulk micro defect density in a region extending from thecenter of the wafer to the edge of the wafer of less than 200%, or in aregion extending from about 10 mm to the edge of the wafer to the edgeof the wafer of less than 100%.

In some aspects of the disclosure, thermally treated wafers sliced fromthe ingots of the present disclosure are characterized by an edge bandextending in a region extending from about 5000 μm, 4000 μm, 3000 μm,2000 μm or 1000 μm to the edge (lateral surface) of the crystal to theedge of the crystal. The edge band is characterized by oxygenprecipitates having an average diameter of from about 30 nm to about 100nm and an oxygen precipitation density of from about 1*10⁸ atoms per cm³to about 1*10¹⁰ atoms per cm³ and by voids having an average radius offrom about 1 nm to about 50 nm. The BDM size and density distribution inthe edge band is substantially similar to the distribution in a regionextending from the central axis to the edge band. In some aspects of thedisclosure, the edge band radial BMD size differs from the BMD size inthe remainder of the wafer by no more than 20%. In some other aspects ofthe disclosure, the edge band BMD density differs from the BMD densityin the remainder of the wafer by no more than 200%

Single crystal silicon ingots may be grown according to the standard CZmethod. Single crystal silicon ingots are grown in a crystal puller.See, e.g., U.S. Pat. No. 6,554,898 and WO 99/27165 (both assigned toSunEdison Semiconductor Technology PTE. Ltd.), the disclosures of whichare incorporated herein as if set forth in their entireties. A typicalCZ puller comprises a housing; a crucible in the housing for containingmolten silicon; a pulling mechanism for pulling a growing ingot upwardfrom the molten silicon; and heating mechanism in proximity to thecrucible sufficient to melt solid silicon starting material (i.e., apolycrystalline charge comprising polycrystalline granules and/or chunkpolycrystalline) into a molten silicon bath. Polycrystalline materialmay be charged to the crucible according to techniques known in the art,e.g., as described in WO 99/55940 (assigned to SunEdison SemiconductorTechnology PTE. Ltd.).

Ingot growth according to the CZ method begins by melting a charge ofsolid silicon starting material by applying power to the heatingmechanism. See, e.g., WO 99/20815 (assigned to SunEdison SemiconductorTechnology PTE. Ltd.). The melt flow may be stabilized by cruciblerotation rate, inert gas flow rate, etc. prior to dipping a seed crystalinto the melt. Pulling the seed upwards crystallizes the melt at thesolid-liquid interface and the crystal proceeds to grow. A conical neckof increasing diameter from the seed crystal is grown by decreasing thepull rate of the seed crystal from the melt. Once the desired diameteris reached, the pull rate is gradually increased until the crystal growsa substantially constant diameter region. The heating mechanisms of thecrystal pulling apparatus are controlled in order to control thesolidification and cooling rate of the growing silicon ingot. Thecrucible is typically rotated in the opposite sense to the crystal tostabilize the melt flow and control the oxygen concentration in thecrystal. The final stage of the crystal growth is the tail growth wherethe diameter is slowly decreased and a conical shape is achieved, inwhich the diameter of the end cone decreases in the axial direction fromthe constant diameter region toward the end of the crystal. Once thecrystal has detached from the melt, the power to the puller is decreasedand the crystal is cooled down while being lifted into an upper chamber.At the end of the process, the crystal is removed from the puller forfurther processing.

Crystal ingots of the present disclosure comprise a central axis, a seedend, an opposite end, and a constant diameter portion between the seedend and the opposite end having a lateral surface and a radius, r,extending from the central axis to the lateral surface, the singlecrystal silicon ingot being grown from a silicon melt and then cooledfrom the solidification in accordance with the CZ method. The singlecrystal silicon ingot is characterized by a constant diameter portioncomprising a radially symmetric region in which vacancies are thepredominant intrinsic point defect, the radially symmetric region havinga radius extending from the central axis to the lateral surface.

Some aspects of the present disclosure are directed to a single crystalsilicon wafer obtained (sliced) from an ingot, as detailed herein above.More particularly, the present disclosure is directed to a singlecrystal silicon wafer having a diameter of from about 150 mm to about450 mm. The wafer preferably has a front surface, a back surface, animaginary central plane between the front and back surfaces andsubstantially parallel to the front and back surfaces, and acircumferential edge joining the front surface and the back surface. Thewafer additionally comprises an imaginary central axis perpendicular tothe central plane and a radial length that extends from the central axisto the circumferential edge. The terms “front” and “back” in thiscontext are used to distinguish the two major, generally planar surfacesof the wafer. The front surface of the wafer (as that phrase is usedherein) is not necessarily the surface onto which an electronic devicewill subsequently be fabricated, nor is the back surface of the wafer(as that phrase is used herein) necessarily the major surface of thewafer which is opposite the surface onto which the electronic device isfabricated. In addition, because silicon wafers typically have sometotal thickness variation (TTV), warp, and bow, the midpoint betweenevery point on the front surface and every point on the back surface maynot precisely fall within a plane. As a practical matter, however, theTTV, warp, and bow are typically so slight that, to a closeapproximation, the midpoints can be said to fall within an imaginarycentral plane which is approximately equidistant between the front andback surfaces. The wafer may be polished or, alternatively, lapped andetched but not polished. Such methods, as well as standard siliconslicing, lapping, etching, and polishing techniques are disclosed, forexample, in F. Shimura, Semiconductor Silicon Crystal Technology,Academic Press, 1989, and Silicon Chemical Etching, (J. Grabmaier ed.)Springer-Verlag, New York, 1982 (incorporated herein by reference).Preferably, the wafers are polished and cleaned by standard methodsknown to those skilled in the art. See, for example, W. C. O'Mara etal., Handbook of Semiconductor Silicon Technology, Noyes Publications.

According to previous publications (see, e.g., WO 98/45507, WO 98/45508,WO 98/45509, and WO 98/45510, all assigned to SunEdison SemiconductorTechnology PTE. Ltd.), the type and initial concentration of intrinsicpoint defects is initially determined as the ingot cools from thetemperature of solidification (i.e., about 1410° C.) to a temperaturegreater than 1300° C. That is, the type and initial concentration ofthese defects are controlled by the ratio v/G, where v is the growthvelocity and G is the average axial temperature gradient over thistemperature range. As the value of v/G increases, a transition fromdecreasingly self-interstitial dominated growth to increasingly vacancydominated growth occurs near a critical value of v/G_(o) which, basedupon currently available information, appears to be about 2.1*10⁻⁵cm²/sK, where G_(o) is determined under conditions in which the axialtemperature gradient is constant within the temperature range definedabove. At this critical value, the concentrations of these intrinsicpoint defects are at equilibrium. As the value of v/G_(o) exceeds thecritical value, the concentration of vacancies increases. Likewise, asthe value of v/G_(o) falls below the critical value, the concentrationof self-interstitials increases.

Thermal treatment cycles typically employed in the fabrication ofelectronic devices can cause the precipitation of oxygen in siliconwafers which are supersaturated in oxygen. Depending upon their locationin the wafer, the precipitates can be harmful or beneficial. Oxygenprecipitates located in the active device region of the wafer can impairthe operation of the device. Oxygen precipitates located in the bulk ofthe wafer, however, are capable of trapping undesired metal impuritiesthat may come into contact with the wafer. The use of oxygenprecipitates located in the bulk of the wafer to trap metals is commonlyreferred to as internal or intrinsic gettering (“IG”).

Oxygen precipitation behavior in CZ silicon material is stronglyinfluenced by intrinsic point defect concentrations. For example inlightly doped material, generally strong precipitation is observed invacancy type material whereas in interstitially type material, noprecipitation occurs. Any thermal treatment sufficient to nucleate andgrow oxygen precipitates is suitable for preparing wafers of the presentdisclosure with uniform and high oxygen precipitates throughout thewafer, i.e., in a region extending from the central axis to thecircumferential edge and further in a region extending from the frontsurface of the wafer to the back surface of the wafer. In someembodiments, the BMD may be characterized by subjecting the wafers to anoxygen precipitation heat-treatment at a temperature in excess of about700° C. for a duration sufficient to nucleate and grow oxygenprecipitates. In some other characterization embodiments, the wafers maybe subjected to an oxygen precipitation heat treatment comprising theNEC1 test procedure, e.g., annealing the wafer for 4-8 hours at 800° C.and then 16 hours at 1000° C. In some other characterizationembodiments, the wafers may be subjected to an oxygen precipitation heattreatment comprising annealing the wafer for 3 hours at 780° C. and then16 hours at 1000° C. In some other embodiments, the wafers are postepitaxial wafers that have been subjected to oxygen precipitation heattreatment wherein the post epitaxial treatment is done at a temperatureof about 900° C., about 950° C., about 1000° C., about 1050° C., about1100° C., about 1150° C., or about 1200° C., and ranges thereof, such asfrom about 900° C. to about 1200° C., from about 1000° C. to about 1200°C., or from about 1050° C. to about 1150° C.

Nitrogen dopant concentration, CZ silicon crystal pull rate, and CZcrystal temperature gradient during pulling affect BMD size anddistribution in thermally treated wafers sliced from the CZ siliconcrystal ingots. In any of the various aspects of the disclosure, the BMDsize distribution, the BMD density distribution and the edge bandcharacteristics of the present CZ silicon crystal ingots and wafers maybe controlled by selection of variables within the ranges describedbelow as determined by the modeling and simulation techniques alsodescribed below. Preferred ranges may suitably vary with ingot diameter.In one embodiment, the nitrogen dopant concentration range is from about1*10¹³ atoms per cm³ to about 1*10¹⁵ atoms per cm³, the pull rage rangeis from about 0.4 mm per minute to about 1.5 mm per minute, and theingot surface temperature gradient is from about 10° K per minute toabout 50° K per minute at an average crystal surface temperature of fromabout 1300° C. to about 1415° C. In one embodiment, for a 300 mmdiameter ingot, the nitrogen dopant concentration range is from about1*10¹³ atoms per cm³ to about 1*10¹⁵ atoms per cm³, the pull rage rangeis from about 0.85 mm per minute to about 1.5 mm per minute, and theingot surface temperature gradient is from about 10° K per cm to about35° K per cm at an average crystal surface temperature of from about1300° C. to about 1415° C.

Nitrogen Dopant Concentration

The silicon crystals of the present disclosure comprise nitrogen dopantatoms that induce a decrease in void size distributions in CZ silicon.Nitrogen concentration affects the radius of as-grown oxygen clusters asa function of crystal radial location. The nitrogen concentration in thesilicon crystal is from about 1*10¹³ atoms per cm³ to about 1*10¹⁵ atomsper cm³ or from about 1*10¹⁴ atoms per cm³ to about 1*10¹⁵ atoms percm³. The ingot may be doped with nitrogen by any of various methodsknown in the art including, for example, introducing nitrogen gas intothe growth chamber and/or adding nitrogen to the polysilicon melt. Theamount of nitrogen being added to the growing crystal is more preciselycontrolled by adding the nitrogen to the polysilicon melt, as such, itis the preferred method. Typical polysilicon melt nitrogenconcentrations are from about 1*10¹⁶ atoms per cm³ to about 1*10¹⁸ atomsper cm³ or from about 1*10¹⁷ atoms per cm³ to about 1*10¹⁸ atoms percm³, or from about 1*10¹⁷ atoms per cm³ to about 5*10¹⁷ atoms per cm³.The amount of nitrogen added to the crystal may be readily determined,for example, by depositing a layer of silicon nitride (Si₃N₄) of a knownthickness on silicon wafers of a known diameter which are introducedinto the crucible with the polysilicon prior to forming the silicon melt(the density of Si₃N₄ is about 3.18 g/cm³).

It is believed that because nitrogen bonds strongly with vacancies (seeM. Kulkarni, Defect Dynamics in the presence of nitrogen in growingCzochralski silicon crystals, Journal of Crystal Growth, Volume 310,pages 324-335 (2008)), lower nitrogen concentration will amount to morefree vacancies which favors formation of voids and hence, oxygenprecipitates become smaller in the interior regions of the crystal. Aspreviously disclosed, nitrogen-doping incudes a void size distributiondecrease in CZ silicon crystals. It is believed that, acting throughvacancy trapping, nitrogen affects point defect formation in the vacancyregion of the crystal, essentially shifts void formation to lowertemperatures, increases the void density, and decreases the void size.Because of the trapping effect of vacancies in nitrogen doped crystals,oxygen precipitations are formed at higher density and larger sizes thanin non-nitrogen doped crystals. Without being held to a particulartheory, it is believed that the nitrogen dopant atoms thermallystabilize the oxygen precipitation nuclei by retarding the diffusion ofthe vacancies in the silicon crystal. Specifically, it is known that asthe growing crystal cools the concentration of vacancies reaches a levelof critical super saturation (i.e., at which point an agglomerationevent occurs) which results in the formation of agglomerated vacancydefects or micro-voids. For example, the super saturation of may occurat a temperature of about 1150-1050° C. As the crystal cools, themicro-voids grow in size because vacancies continue to diffuse to thesites. Although the agglomeration event and continued growth of themicro-voids significantly reduces the concentration of non-agglomerated,or “free,” vacancies in the crystal, upon continued cooling a secondlevel of critical super saturation is reached in which the freevacancies and oxygen in the crystal interact to form oxygenprecipitation nuclei. For a non-nitrogen doped crystal, the second levelof critical super saturation occurs as the crystal cools below about700° C. In nitrogen doped silicon, however, the formation of micro-voidsduring the agglomeration event is slightly suppressed due to the slowerdiffusion rate of the vacancies. This results in a higher concentrationof free vacancies remaining in the crystal after the first agglomerationevent. The increased concentration of free vacancies in the nitrogendoped silicon increases the temperature at which the second level ofcritical super saturation occurs, e.g., at about 800° C. to about 1050°C. At the increased temperature, the oxygen atoms in the crystal aremore mobile and more oxygen atoms interact with the free vacancies whichresults in oxygen precipitation nuclei which are more stable. Thestabilized oxygen precipitation nuclei are more resistant to dissolutionduring subsequent thermal processing such as the growth of an epitaxialsilicon layer.

As depicted in FIGS. 7 and 8, close to the edge, due to the presence ofthe surface-induced effects, the predicted oxygen precipitate sizes arenot similarly compensated. Particularly, as shown in FIG. 7, nitrogenconcentration affects the radius of as-grown oxygen clusters as afunction of crystal radial location resulting in an uneven distributionof radius size wherein, for a 300 mm diameter ingot, oxygen clusterradii increases dramatically at the edge region. As shown in FIG. 8,nitrogen concentration affects the radius of as-grown voids as afunction of crystal radial location resulting in an uneven distributionof radius size wherein, for a 300 mm diameter ingot, void size radiidecreases dramatically at the edge region.

The dependence of average BMD density resulting from the effect ofnitrogen concentration is believed to be independent of annealingtemperature. As depicted in FIG. 9, the predicted average BMD densityvaried from about 9.1*10⁷ per cm³ at an ingot nitrogen concentration ofabout 7.5*10¹³ atoms per cm³ to about 4.1*10⁸ per cm³ at an ingotnitrogen concentration of about 2.5*10¹⁴ atoms per cm³ at an annealingtemperature of 1100° C. As depicted in FIG. 10, the predicted averageBMD density varied from about 2.15*10¹⁰ per cm³ at an ingot nitrogenconcentration of about 7.5*10¹³ atoms per cm³ to about 3.75*10¹⁰ per cm³at an ingot nitrogen concentration of about 2.5*10¹⁴ atoms per cm³ at anannealing temperature of 1000° C. Although the average BMD density wasgreater at 1000° C. than at 1100° C., the dependence of average BMDdensity based on nitrogen concentration was similar at bothtemperatures.

Pull Rate

As shown in FIG. 3, pull rate affects the predicted radius of as-grownoxygen clusters as a function of crystal radial location resulting in anuneven distribution of radius size. For pull rates on the order of about0.78 mm/min for a 300 mm diameter ingot, oxygen cluster radii increasesdramatically at the edge region. As shown in FIG. 4, pull rate affectsthe predicted radius of as-grown voids as a function of crystal radiallocation resulting in an uneven distribution of radius size wherein, fora 300 mm diameter ingot, void size radii decreases dramatically at theedge region at pull rates of 0.7 mm/min or greater. The data upon whichFIGS. 3 and 4 are based was obtained for a constant oxygen concentrationof 5.5*10¹⁰ atoms/cm³ and a nitrogen concentration of 1.26*10¹⁴atoms/cm³ across the cross-section. For each pull rate, the crystalsurface temperature gradient close to the melt/crystal interface was51.14° K/cm. The in-grown vacancies in the crystal can agglomerate intovoids as well as facilitate formation of oxygen clusters as the crystaltemperature drops. There is a peak in the size profiles of both vacancyclusters as well as oxygen clusters, found for each case, close to thecrystal surface. At high pull rate values, the edge peak for voids sizeis much less steeper than the one observed for the oxygen clusters. Thisobservation is consistent with the established theory on lateralincorporation effect. At a lower pull rate, less vacancies areincorporated everywhere, which delays void formation but, in the vacancydominated crystal, at these high crystal pull rates, can facilitateformation of oxygen clusters earlier. Therefore, it is the competitionbetween void formation and oxygen cluster formation depending on thefree vacancy concentration, which is determined based on axialincorporation, strength of bonding with oxygen and nitrogen, and lateralincorporation, which needs to be tailored to increase the uniformity inthe size distribution of oxygen clusters. Increasing the pull ratebrings in enough vacancies everywhere, increasing the void sizes andlowering the oxygen cluster sizes. It has been discovered that the edgeband of oxygen precipitation decreases dramatically in its intensitywhen pull rate is increased to about 0.95 mm/min or even 1 mm/min.

Pull rate ranges within the scope of the present disclosure vary withingot diameter and are generally from about 0.4 to about 1.5 mm/min,from about 0.5 to about 1.5 mm/min, from about 0.6 to about 1.5 mm/min,from about 0.7 to about 1.5 mm/min. Rates within the scope of thepresent disclosure include about 0.4 mm/min, about 0.5 mm/min, about 0.6mm/min, about 0.7 mm/min, about 0.78 mm/min, about 0.8 mm/min, about0.85 mm/min, about 0.9 mm/min, about 1.0 mm/min, about 1.1 mm/min, about1.2 mm/min, about 1.3 mm/min, about 1.4 mm/min, about 1.5 mm/min, andranges thereof. For instance, A pull rate of from about 0.85 mm/min toabout 1.5 mm/min, from about 0.85 mm/min to about 1.0 mm/min or fromabout 0.9 mm/min to about 1.0 mm/min is generally preferred for a 300 mmingot. Pull rate ranges for ingots having a diameter in excess of 300mm, such as about 400 mm or about 450 mm are preferably less than about0.8 mm/min, such as from about 0.4 to about 0.7 mm/min, from about 0.5to about 0.7 mm/min, or from about 0.5 to about 0.6 mm/min. Pull ratesthat provide for v/G in excess of the critical value according to theVoronkov theory are preferred.

The average BMD density was found to be a function of the pull ratewherein the characteristics of this functionality changes depending uponthe annealing temperature. For instance, as shown in FIG. 5, at anannealing temperature of 1100° C., the predicted average BMD density fora 300 mm ingot is about 2 orders of magnitude lower than for anannealing temperature of 1000° C., and it decreases with increase inpull rate. As shown in FIG. 6, the predicted average BMD density for a300 mm ingot is about 2 orders of magnitude greater than for the 1100°C. annealing temperature and increases with increasing pull rate up to0.95 mm/min and drops slightly at 1 mm/min.

Temperature Gradient

The average axial temperature gradient to which a growing CZ crystal isexposed affects the void size distribution across a crystalcross-section from the central axis to the edge. Generally, void sizeincrease is inversely proportion to temperature gradient such that thevoid size increases especially close to the crystal edge in response toa reduction in the temperature gradient at the crystal edge close to themelt/crystal interface. This predicted effect is depicted in FIGS. 11and 12. This, in effect, helps to diminish the size of oxygenprecipitates close to the crystal edge while the oxygen precipitate sizein the interior of the crystal is substantially unaffected bytemperature gradient.

The reduction in temperature gradient on the crystal surface close tothe melt/crystal interface can be made by exposing that part more tohotter sections of the hot zone. For example, one way of achieving thisis by increasing the gap between melt surface and the bottom of thereflector graphite (also known as “Hr”). Another method is to increasethe side heater power by running higher bottom heater power.

Temperature gradients ranges within the scope of the present disclosureare from about 10° K to about 50° K per cm, from about 10° K to about35° K per cm, from about 25° K to about 50° K per cm, from about 25° Kto about 45° K per cm, from about 30° K to about 45° K per cm, or fromabout 35° K to about 45° K per cm at an average crystal surfacetemperature of from about 1300° C. to about 1415° C. Temperaturegradients include about 10° K per cm, about 20° K per cm, about 25° Kper cm, about 30° K per cm, about 35° K per cm, about 40° K per cm,about 45° K per cm, about 50° K per cm, and various ranges thereof.

The dependence of average BMD density resulting from the effect oftemperature gradient is believed to be minimally related to annealingtemperature. As depicted in FIG. 13, the predicted average BMD densityfor a 300 mm ingot varied from about 2*10⁸ per cm³ at a crystal surfacetemperature gradient of about 31 K/cm to about 2.25*10⁸ per cm³ at acrystal surface temperature gradient of about 51 K/cm at an annealingtemperature of 1100° C. As depicted in FIG. 14, the predicted averageBMD density for a 300 mm ingot varied from about 2.8*10¹⁰ per cm³ at acrystal surface temperature gradient of about 31 K/cm to slightly lessthan about 2.8*10¹⁰ per cm³ at a crystal surface temperature gradient ofabout 51 K/cm at an annealing temperature of 1000° C. Although theaverage BMD density was greater at 1000° C. than at 1100° C., thedependence of average BMD density based on ingot nitrogen concentrationwas substantially similar at both temperatures.

Combinations of Pull Rate, Surface Temperature Gradient and NitrogenConcentration

In accordance with the present disclosure, it has been discovered thatcombinations of pull rate, surface temperature gradient and nitrogenconcentration affect (i) the radial uniformity of vacancy radius anddensity as a function of crystal radial location across the crystalcross section, (ii) radial uniformity of BMD diameter and density as afunction of crystal radial location across the crystal cross section ofthermally treated wafers sliced from the nitrogen-doped CZ siliconcrystals, and (iii) edge band characteristics of said wafers. It hasbeen further discovered that combinations of pull rate, surfacetemperature gradient and nitrogen concentration may be selected toachieve a substantial radial uniformity of BMD diameter and density as afunction of crystal radial location across a crystal wafer cross sectionand a substantial absence of an edge effect. Various algorithms, andcombinations thereof, as described herein, have been employed to model(i) the effect of pull rate and temperature gradient on BMD size anddensity distribution, (ii) the effect of oxygen concentration andnitrogen concentration together with pull rate and temperature gradienton BMD size and density distribution, (iii) the BMD size distributionbased on the lumped model, and (iv) the edge band characteristics.

In further accordance with the present disclosure, combinations of pullrate, nitrogen concentration and crystal surface temperature gradientwere evaluated by simulation and experimentation in order to derive aset of conditions suitable for the preparation of nitrogen doped CZsilicon crystal ingots characterized by substantial radial uniformity ofvacancy radius and density as a function of crystal radial locationacross the crystal cross section and thermally treated wafers slicedtherefrom characterized by substantial radial uniformity of BMD diameterand density as a function of crystal radial location across the crystalcross section, wherein the wafer exhibits the essential absence of anedge effect. More particularly, utilizing the defect simulation modelsdisclosed herein, it is possible to predict the contribution from somekey parameters to the agglomeration of vacancies and oxygen clusteringin silicon crystals and wafers for a given diameter. In the simulationmodels, in one embodiment for a 300 mm diameter wafer, the presence ofoxygen precipitation band in the vicinity of a silicon wafer at highpull rates of 0.78 to 1.0 mm/min was addressed. This findingcorroborates the lateral incorporation of vacancies effect disclosed byKulkarni (U.S. Pat. No. 8,216,362). The effect of these changes on theaverage BMD density averaged over lateral cross-section in wafers slicedfrom as grown crystals after various thermal treatments, which can besimulated as Epi and annealing, is also addressed by the simulations.Based on the simulation results, various combinations of these keyparameters were designed and evaluated. The simulation models were usedto assess the combined effects of the parameters and to establish abasis from which to test crystal growth and evaluate wafers in order tocalibrate the simulation models and to confirm the final results.Several iterations of simulation, calibration, and testing were done inorder to achieve radial uniformity of BMD in controlled size and densitycrystal ingots, polished, and Epi wafers. The simulation results wereexperimentally validated. It is to be noted that BMD size for purposesof simulation is estimated on the basis of radius, while BMD size inthermally treated or post epi thermally treated wafers is on the basisof diameter.

Based on simulation and experimentation, a correlation between wafer BMDand each the CZ silicon ingot individual parameters including nitrogenconcentration, crystal pull rate and temperature gradient has beenestablished. To achieve satisfactory BMD capabilities in polished, Epi,and annealed wafers, interrelationships between the various parametersdisclosed herein have been established by simulation models to enableprediction of the outcome of various combinations of the parameters inorder to achieve desired and optimized precipitation behavior withuniform radial distribution of BMD in controlled size and density inwafers without substantial edge effect.

Based on simulations and experimental evaluation, a combination ofvariables sufficient to achieve the objects of the present disclosurehas been established. The ranges may suitably vary with ingot diameter.In any of the various aspects of the present disclosure for thepreparation of CZ silicon crystal ingots: (1) the nitrogen concentrationis from about 1*10¹³ atoms per cm³ to about 1*10¹⁵ atoms per cm³; (2)the temperature gradient is from about 10° K per cm to about 50° K perminute, from about 10° K per minute to about 35° K per cm, from about25° K per cm to about 50° K per cm, from about 30° K per cm to about 50°K per cm, or from about 35° K per cm to about 50° K per cm; and (3) thepull rate is from about 0.4 mm per minute to about 1.5 mm per minute,from about 0.5 mm per minute to about 1.5 mm per minute, from about 0.85mm per minute to about 1.5 mm per minute, from about 0.7 mm per minuteto about 1.0 mm per minute, from about 0.78 mm per minute to about 1.0mm per minute, from about 0.8 mm per minute to about 1.0 mm per minute,from about 0.85 mm per minute to about 1.0 mm per minute, from about0.75 mm per minute to about 1.0 mm per minute, or from about 0.9 mm perminute to about 1.0 mm per minute. In some 300 mm diameter CZ siliconcrystal ingot aspects, a combination of variables selected from a pullrate of from about 0.85 mm per minute to about 1.5 mm per minute, atemperature gradient of from about 10° K per cm to about 35° K per cm atan average crystal surface temperature of from about 1300° C. to about1415° C., and a nitrogen concentration of from about 1*10¹³ atoms percm³ to about 1*10¹⁵ atoms per cm³ provides for an ingot having the BMDsize and density distributions and edge band characteristics asdescribed herein. In some other such aspects, the pull rate is fromabout 0.85 mm per minute to about 1.0 mm per minute or form about 0.9 mmper minute to about 1.0 mm per minute. For CZ silicon crystals having adiameter of other than 300 mm, the combination of pull rate range,nitrogen concentration range, and temperature gradient range required toachieve the BMD distribution and edge band objects of the presentdisclosure may be determined by the simulations disclosed herein whereinthe predicted ranges may fall outside, overlap or be encompassed by theranges required for a 300 mm diameter ingot.

Simulations

Algorithms and simulation methods are disclosed herein that allow forthe prediction of a set of pull rate, nitrogen concentration andtemperature gradient variables for a given CZ silicon crystal ingotdiameter that enable the preparation of nitrogen doped CZ silicon wafershaving the radially uniformly distributed BMD diameter and density, andthe edge band characteristics disclosed herein.

An algorithm used to model and predict the effect of pull rate andtemperature gradient on BMD size and distribution is disclosed by M. S.Kulkarni and V. V. Voronkov, Simplified Two-Dimensional Quantificationof the Grown-in Microdefect Distributions in Czochralski Grown SiliconCrystals, Journal of the Electrochemical Society, 152 (10) pages G781 toG786 (2005), referenced herein as the “Kulkarni 2005 Algorithm”. Thedisclosed lumped model allows for computationally prediction of BMDdistributions in thermally treated wafers. In summary, the microdefectscan be approximated as spherical clusters. At an element of a CZcrystal, an equivalent population of identical clusters of the sameradius, equal to the average radius of the actual cluster population,represents the actual cluster population. By replacing the averagecluster radius by the square root of the average of the squared radii ofthe clusters, the equations describing the defect dynamics can becomputationally simplified. The microdefect distribution is quantifiedby a set of disclosed equations describing the point defectconcentration (C), the cluster density (N), and an auxiliary variable(U) proportional to the surface area of the total cluster population.The cluster density N is predicted by the classical nucleation theory, Uis described using the disclosed cluster growth equation, and C by thedisclosed equation involving the transport, the recombination, and theconsumption by the growing clusters of the point defects. The model issufficiently accurate to capture the final (grown-in) spatialdistribution of the microdefect density and size and was validated bycomparison of the predictions of the model with the predictions of arigorous model and the experimental observations.

An algorithm used to model and predict the effect of nitrogenconcentration, pull rate and temperature gradient on BMD size anddistribution is disclosed by M. S. Kulkarni, Defect dynamics in thepresence of nitrogen in growing Czochralski silicon crystals, Journal ofCrystal Growth 310, pages 324 to 335 (2008), referenced herein as the“Kulkarni 2008 Algorithm”. The disclosed model approximates allaggregates as spherical clusters. As disclosed by Kulkarni, classicalnucleation theory captures the formation of all clusters with areasonable accuracy. The formed clusters grow by diffusion-limitedkinetics. Vacancy clusters and self-interstitial clusters are formed bythe homogeneous nucleation of vacancies and self-interstitials,respectively. Oxygen clusters, because of their higher specific volume,are formed by the facilitation by vacancies. The growth of oxygenclusters is limited by the diffusion of oxygen when vacancies are inabundance and by the diffusion of vacancies when vacancies are scarce.The population of clusters at a given location in a growing crystal isapproximated by an equivalent population of identical clusters. Themodel quantifies the conditions leading to the formation of differentmicrodefects in CZ crystal growth. The effects of varying pull-rate andthe nitrogen concentration are also captured. The model quantifies themicrodefect distributions in CZ crystals growing under both steadystates as well as unsteady states. The disclosed model predictions agreewell with the reported microdefect distributions in the presencenitrogen in low to moderately high concentrations. In the presence ofnitrogen in very high concentrations (on the order of 10¹⁸ cm⁻³ ormore), however, the model predictions are less accurate.

An algorithm used to model and predict the effect of oxygenconcentration, pull rate and temperature gradient on BMD size anddistribution is disclosed by M. S. Kulkarni, Defect dynamics in thepresence of oxygen in growing Czochralski silicon crystals, Journal ofCrystal Growth 303, pages 438 to 448 (2007), referenced herein as the“Kulkarni 2007 Algorithm”. The disclosed model quantifies thedistributions of microdefects in growing CZ crystals can be accomplishedby treating reactions involving the intrinsic point defects of siliconand oxygen, along with the formation and growth of microdefects. Thepresence of oxygen primarily generates two bound vacancy species, vO andvO₂, and aggregates of oxygen. The aggregates of vacancies are modeledas spherical v-clusters; the aggregates of self-interstitials aremodeled as spherical i-clusters; and the aggregates of oxygen, primarilysilicon dioxide, are modeled as spherical O-clusters. The complexity ofthis treatment is reduced by the application of the lumped modeldeveloped by Kulkarni and Voronkov, (Simplified Two-DimensionalQuantification of the Grown-in Microdefect Distributions in CzochralskiGrown Silicon Crystals, Journal of the Electrochemical Society, 152 (10)pages G781 to G786 (2005)) that approximates a population of clusters ofdifferent sizes at any given location in a CZ crystal as an equivalentpopulation of identical clusters. The key element of the disclosed modelis the vacancy assisted formation of O-clusters. Effectively, all largeO clusters in the CZ growth are formed by absorbing vacancies, as thespecific volume of O-clusters is greater than that of silicon. Thegrowing O-clusters directly consume only free vacancies (v); as the freevacancy concentration decreases, however, more free vacancies aregenerated by the disassociation of vO and vO₂ species. Thus, both freevacancies and vacancies bound in vO and vO₂ species are consumed.

The disclosed model quantifies the microdefect distributions in CZcrystals growing under steady states as well as unsteady states. It isbelieved that the type of microdefect formed in a given region in thecrystal depends on the concentration of the intrinsic point defects andof vO and vO₂ species established a short distance away from theinterface. In the regions marked by a high free vacancy concentration,voids or v-clusters are formed at higher temperatures by the nucleationof vacancies. The v-cluster growth consumes both free and boundvacancies. In the regions marked by a moderate free vacancyconcentration, v-cluster formation is suppressed at higher temperatures;free and bound vacancies are consumed by the formation and growth ofO-clusters. The binding between vacancies and oxygen allows survival ofvacancies in the bound form in very low concentrations at lowertemperatures even in the presence of v-clusters and O-clusters. In theregions marked by the dominance of self-interstitials, i-clusters areformed.

The concentration fields of the intrinsic point defects in the vicinityof the interface is believed to be established primarily by theinterplay between the Frenkel reaction and the intrinsic point defecttransport. Oxygen increases the effective vacancy concentrationavailable for the recombination with self-interstitials by increasingthe concentration of vO and vO₂ species and marginally aids theconditions leading to the survival of vacancies as the dominantintrinsic point defect species, for fixed crystal growth conditions. Theincrease in the pull-rate range within which crystals free of largev-clusters and i-clusters can be grown, with increasing oxygenconcentration, is also predicted and explained by the model. Thisbehavior is caused by an increase in the concentration of boundvacancies with increasing oxygen concentration, for fixed crystal growthconditions. Qualitative microdefect distributions in CZ crystalsreported in the literature can be quantified by the developed model.

An algorithm used to model and predict the BMD size distribution basedon the lumped model is disclosed by G. Samanta and M. S. Kulkarni,Efficient computation of population distribution of microdefects at anylocation in growing Czochralski silicon single crystals, Journal ofCrystal Growth, 393, pages 49 to 53 (2014), referenced herein as the“Samanta Algorithm”. The disclosed model is based on the model describedin M. S. Kulkarni and V. V. Voronkov (Simplified Two-DimensionalQuantification of the Grown-in Microdefect Distributions in CzochralskiGrown Silicon Crystals, Journal of the Electrochemical Society, 152 (10)pages G781 to G786 (2005)) and allows for calculation of sizedistribution of microdefect population at any location in the crystalwithout taking cluster formation and path (migration) energies intoaccount. The dependences of thermal stress and dopant concentration arealso not taken into account. The dopant-induced strain effect onintrinsic point defect equilibrium concentrations is negligibly smallfor conventional doping levels. The change in equilibrium values ofpoint defect concentrations due to dopant-induced shift in the Fermilevel is also significant only at very high doping levels (of the orderof 10¹⁸ cm⁻³ or more). The impact of thermal stress on equilibriumconcentration values is also small. The computational advantage of thelumped model is not compromised when the point defect concentrationfield evolved through it is also used to solve for the size distributionof microdefect populations at chosen locations in the crystal. The sizedistributions predicted from lumped model agree reasonably well withthose predicted from rigorous model under steady as well as unsteadyconditions.

In accordance with the present disclosure, a method has been developedbased on the above-described algorithms for deriving pull rate,temperature gradient and nitrogen concentration values enabling thepreparation of single crystal CZ silicon characterized by substantialradial uniformity of vacancy radius and density as a function of crystalradial location across a crystal cross section, by substantial radialuniformity of BMD diameter and density as a function of crystal radiallocation across a crystal cross section, and by the substantial absenceof an edge effect has been developed. One such embodiment is depicted inthe FIG. 23 flow chart. In summary, The Kulkarni 2005, Kulkarni 2007,and Kulkarni 2008 algorithms are used in combination with the Samantaalgorithm to simulate the radial profile of oxide precipitate densityand size and to evaluate the edge band characteristics of single crystalCZ silicon ingots and wafers. For any given set of pull rate,temperature gradient and nitrogen concentration variables, siliconcrystals ingots or wafers are deemed to be unacceptable if they arepredicted by simulation to fail because of (i) an increase in radialbulk micro defect size in a region extending from the center of theingot or wafer to the edge of the ingot or wafer of greater than 20%,(ii) an increase in radial bulk micro defect density in a regionextending from the center of the ingot or wafer to the edge of the ingotor wafer of greater than 200%, (iii) an increase in radial bulk microdefect size in a region extending from about 10 mm to the edge of theingot or wafer to the edge of the ingot or wafer of greater than 15%,(iv) an increase in radial bulk micro defect density in a regionextending from about 10 mm to the edge of the ingot or wafer to the edgeof the ingot or wafer of greater than 100%, and (v) an edge band in aregion extending from about 1000 μm to the edge of the ingot or waferand the edge of the ingot or wafer wherein the edge band comprisesoxygen precipitates having an average radius of less than about 30 nm orgreater than about 100 nm and an oxygen precipitation density of lessthan about 1*10⁸ atoms per cm³ or greater than about 1*10¹⁰ atoms percm³. If a set of variables is predicted to result in an unacceptableingot or wafer, then a subsequent simulation iteration is done based ona new set of variables. Simulation iterations are continued until a setof variables is derived that is predicted to provide the desired BMDsize and distribution.

In some further aspects of the present disclosure, the BMD size may bepredicted from simulation. First, the cluster size distribution ofoxygen precipitates is calculated at a number of radial locations acrossthe crystal cross-section at an axial position. Next, a critical size(R_(cr)) is determined based on classical nucleation theory (CNT) asfollows:

R _(cr)=(2215)/(T ln(C _(O) /C _(oe)))  (1)

In equation (1), R_(cr) is in nanometers (nm); T denotes the annealingtemperature in degrees Kelvin; C_(O) denotes oxygen level in thecrystal; and C_(Oe) denotes the equilibrium value of oxygenconcentration in silicon crystal at the temperature T. Density of oxygenprecipitates with sizes greater than R_(cr) is integrated at everylocation and then number averaged over all those locations to estimatethe BMD density.

The present disclosure is further directed to methods for simulatingoxide precipitation density across the wafer depth during annealing. Themathematical model for the simulation is based on the nucleation modelof Voronkov and Falster (Nucleation of oxide precipitates invacancy-containing silicon, Journal of Applied Physics, Volume 51, pages5802-5810 (2002)) wherein the following equations are believed to governthe point defect balance, interaction between vacancy and oxygen, andthe growth of precipitates. The equations are as follows:

ô(C _(vt) −C _(i))/ôt=D _(v)(T)ô ² C _(v) /ôx ² −D _(i)(T)ô ² C _(i) /ôx² −J _(i)  (2)

Equation (2) describes the balance of point defects accounting for thebound as well as free states of vacancies, diffusion fluxes of pointdefects and emission flux of self-interstitials due to the growing oxideprecipitates. The consumption flux of free vacancies can be neglected asit estimated to be less than the diffusion-limited value.

J _(i)=ε4πDC∫I _(s)(t′)R(t′,t)dt′  (3)

Equation (3) gives the quantitative evaluation of the emission flux ofself-interstitials.

R(t′,t)=[2DC(t−t)/q] ^(1/2)  (4)

Equation (4) describes the diffusion limited growth of nucleated oxideprecipitates.

C _(i) C _(vt) =C _(ie) C _(vte)  (5)

Equation (5) is a result of the reasonable assumption of fast reactionbetween bound as well as free vacancies and self-interstitials.

C _(v) /C _(vt) =C _(ve) /C _(vte)  (6)

Equation (6) arises from the assumption that free vacancies are quicklycaptured by the oxygen clusters.

Simulations of annealing a wafer of 600 micron thickness containing8*10¹⁷ oxygen atoms per cm³ and an initial total vacancy concentration(C_(vt)) of 6*10¹² numbers per cm³ at 800° C. for 1 hour were done. Theselected C_(vt) value is considered to be a typical value for vacancydominated wafers as measured using Pt diffusion technique. FIG. 19 is agraph of the predicted oxide precipitate density across the wafer depthat various times during annealing. FIG. 20 is a graph of predictedC_(vt) across the wafer depth at various times during annealing. FIGS.19 and 20 show the changes that happen close to the wafer surface due tothe presence of equilibrium conditions on the surface. The total vacancyconcentration out-diffuses from the bulk towards the wafer surfacecausing the precipitate density to also decay away from the bulk. At adepth of about 30 to 40 microns from the wafer surface, precipitatedensity remains low compared to the bulk value.

Silicon wafers of the present disclosure may be used in a variety ofapplications. For example, such wafers having a bare silicon surfacepolished to a specular finish (i.e., a polished wafer) may be useddirectly in an integrated circuit manufacturing process. Alternatively,the wafer may be used as a substrate for epitaxial deposition or siliconon insulator (“SOI”) (by layer transfer or oxygen implantation). Ifdesired, the near-surface region of the wafers, e.g., generally up toabout 2 micrometers, may be substantially, or even entirely, removed bychemical etching using etchants and techniques conventional in the art.If desired, the wafer may be chemically or chemomechanically polished toa specular finish prior to or after oxygen precipitation. The epitaxiallayer may be deposited onto the entire wafer, or, alternatively, ontoonly a portion of the wafer. The epitaxial layer preferably is depositedonto the front surface of the wafer. More preferably, it is depositedonto the entire front surface of the wafer. Whether it is preferred tohave an epitaxial layer deposited onto any other portion of the waferwill depend on the intended use of the wafer. For most applications, theexistence or nonexistence of an epitaxial layer on any other portion ofthe wafer is not critical.

A silicon on insulator structure generally comprises a device layer, ahandle wafer or supporting layer, and an insulating film or layer(typically an oxide layer) between the supporting layer and the devicelayer. Generally, the device layer is between about 0.5 and 20micrometers thick. Silicon on insulator structures may be prepared usingvarious techniques known in the art, such as SIMOX or BESOI. SOIstructures may be prepared, for example, by the SIMOX process bysubjecting the wafer to an ion implantation process which is standard inthe art. (See, e.g., U.S. Pat. No. 5,436,175 and Plasma Immersion IonImplantation for Semiconductor Processing, Materials Chemistry andPhysics 46 (1996) 132-139, both of which are incorporated herein byreference). SOI structures may also be prepared by bonding two wafersand removing a portion of one of the bonded wafers. For example, SOIstructures can be prepared by the BESOI process, wherein the wafer isbonded to another wafer, and then a substantial portion of one of thewafers is etched away using known wafer thinning techniques to obtainthe device layer. (See, e.g., U.S. Pat. Nos. 5,024,723 and 5,189,500which are incorporated herein by reference.)

The epitaxial deposition preferably is carried out by chemical vapordeposition. Generally speaking, chemical vapor deposition involvesexposing the surface of the wafer to an atmosphere comprising silicon inan epitaxial deposition reactor, e.g., a Centura reactor available fromApplied Materials. Preferably, the surface of the wafer is exposed to anatmosphere comprising a volatile gas comprising silicon (e.g., SiCl₄,SiHCl₃, SiH₂Cl₂, SiH₃Cl, or SiH₄). The atmosphere also preferablycontains a carrier gas (preferably H₂). For example, the source ofsilicon during the epitaxial deposition may be SiH₂Cl₂ or SiH₄. IfSiH₂Cl₂ is used, the reactor vacuum pressure during depositionpreferably is from about 500 to about 760 Torr. If, on the other hand,SiH₄ is used, the reactor pressure preferably is about 100 Torr. Mostpreferably, the source of silicon during the deposition is SiHCl₃. Thistends to be much cheaper than other sources. In addition, an epitaxialdeposition using SiHCl₃ may be conducted at atmospheric pressure. Thisis advantageous because no vacuum pump is required and the reactorchamber does not have to be as robust to prevent collapse. Moreover,fewer safety hazards are presented and the chance of air or other gasesleaking into the reactor chamber is lessened.

During the epitaxial deposition, the temperature of the wafer surfacepreferably is ramped to and maintained at a temperature sufficient toprevent the atmosphere comprising silicon from depositingpolycrystalline silicon on the surface. Generally, the temperature ofthe surface during this period preferably is at least about 900° C. Morepreferably, the temperature of the surface is maintained in the range ofbetween about 1050 and about 1150° C. Most preferably, the temperatureof the surface is maintained at the silicon oxide removal temperature.The rate of growth of the epitaxial deposition preferably is from about0.5 to about 7.0 μm/min. A rate of about 3.5 to about 4.0 μm/min may beachieved, for example, by using an atmosphere consisting essentially ofabout 2.5 mole % SiHCl₃ and about 97.5 mole % H₂ at a temperature ofabout 1150° C. and an absolute pressure of up to about 1 atm.

In some applications, the wafers comprise an epitaxial layer whichimparts electrical properties. In some embodiments, the epitaxial layeris lightly doped with phosphorous. Therefore, the ambient for epitaxialdeposition comprises phosphorous present as a volatile compound, suchas, for example, phosphine, PH₃. In some embodiments, the epitaxiallayer can contain boron. Such a layer may be prepared by, for example,including B₂H₆ in the atmosphere during the deposition. Epitaxialdeposition typically requires a post epi cleaning step followingepitaxial deposition to remove byproducts formed during the epitaxialdeposition. This step is used to prevent time dependent haze, whichresults if such byproducts react with air. In addition, many post epicleaning techniques tend to form a silicon oxide layer on the epitaxialsurface which tends to passivate (i.e., protect) the surface. Theepitaxial wafers of the present disclosure may be cleaned by methodsknown in the art.

The wafer surfaces may comprise an oxide or nitride layer. For example,a silicon oxide layer forms on a silicon surface when it is exposed toair at room temperature and generally has a thickness of from about 10to about 15 Å. Preferably, the nitride, oxide, or nitride/oxide layer isremoved from the surface of the wafer before the epitaxial layer isdeposited onto the surface. Removal of a silicon oxide or nitride/oxidelayer may be accomplished by heating the surface of the wafer in anoxidant free atmosphere until the oxide or nitride/oxide layer isremoved from the surface. For example, the surface of the wafer ispreferably heated to a temperature of at least about 1100° C., and morepreferably to a temperature of at least about 1150° C. This heatingpreferably is conducted while exposing the surface of the wafer to anatmosphere comprising H₂ or a noble gas (e.g., He, Ne, or Ar). Morepreferably, the atmosphere comprises H₂. Most preferably, the atmosphereconsists essentially of H₂ because use of other atmospheres tends tocause etch pits to form in the surface of the wafer. Generally, it ispreferable to heat the wafer surface to remove the silicon oxide ornitride/oxide layer and then initiate silicon deposition less than 30seconds (more preferably within about 10 seconds) after the oxide ornitride/oxide is removed. Generally, this may be accomplished by heatingthe wafer surface to a temperature of at least about 1100° C. (morepreferably at least about 1150° C.) and then initiating the silicondeposition less than 30 seconds (more preferably within about 10seconds) after the wafer surface reaches that temperature. Waiting toinitiate silicon deposition for up to about 10 seconds after removal ofthe silicon oxide or nitride/oxide layer allows the temperature of thewafer to stabilize and become uniform.

Alternatively, the oxide or nitride/oxide layer may be chemicallystripped. In embodiments where the silicon surface has a nitride/oxidelayer, chemical stripping is the preferred means for removing thenitride/oxide layer. Chemical stripping may be done by means known inthe art using phosphoric acid, hydrofluoric acid, or other acids as areknown. In another alternative, the oxide or nitride/oxide layer may beetched by plasma etching, using, for example, eMAX from AppliedMaterials, or other methods as are known in the art. In embodimentswhere the surface layer is predominantly a silicon nitride layer, thenitride layer may be removed by polishing, chemical etching, or plasmaetching (such as eMAX from Applied Materials, or other etching methodsas are known in the art).

EXAMPLES Example 1

Simulations were done to derive a set of variables that enable thepreparation of 300 mm diameter wafers sliced from nitrogen-doped singlecrystal silicon ingots wherein the wafers are characterized bysubstantial radial uniformity of BMD size and distribution. Thesimulations were based on method depicted in FIG. 23 for the combinationof variables disclosed in Table 1 wherein “Comb” refers to combination,“Prior Art” is a comparative prior art ingot. The nitrogen concentrationin Table 1 refers to concentration in the silicon melt, wherein thenitrogen concentration in a formed silicon crystal is expected to be inthe range of from about 1*10¹³ atoms per cm³ to about 1*10¹⁵ atoms percm³.

TABLE 1 Pull Rate Nitrogen Crystal Surface Temperature Comb. (mm/min)(atoms/cm³) Gradient (K/cm) Prior Art 0.85 1.26 * 10¹⁷ 51.14 1 0.91.76 * 10¹⁷ 46.04 2 0.9 1.26 * 10¹⁷ 46.04 3 0.9 1.76 * 10¹⁷ 35.84 4 0.91.26 * 10¹⁷ 35.84

The radii of as-grown oxygen precipitates and radii of as-grown voids atvarious locations across the wafer cross section from the central axisto the edge was predicted using the simulation method disclosed herein.FIG. 15 is a graph showing the predicted radii of as-grown oxygenprecipitates as a function of radial location across a wafercross-section and FIG. 16 is a graph showing the predicted radii ofas-grown voids as a function of radial location across a wafercross-section. Table 2 below presents the FIG. 15 simulation results intable form for the predicted BMD size percent increase (i) from thecenter of the wafer to the edge of the wafer and (ii) from 10 mm to theedge of the wafer.

TABLE 2 % Oxygen precipitate size % Oxygen precipitate size increasefrom the center of the increase from 10 mm to edge of Comb. ingot to theedge of the ingot the ingot and the edge of ingot 0 39% 34% 1 18% 23% 220% 20% 3 12% 15% 4 17% 15%

BMD density in wafers resulting from high temperature annealing at 1100°C. and 1000° C. was predicted based on simulation. The simulationresults are depicted in FIGS. 17 and 18 where combination 0 refers tothe prior art combination. FIG. 17 is a graph showing the predictedaverage BMD density for wafers as a function of crystal surfacetemperature gradient for constant high temperature annealing done at1100° C. and FIG. 18 is a graph showing the predicted average BMDdensity for wafers as a function of crystal surface temperature gradientfor constant high temperature annealing done at 1000° C.

Example 2

Three 300 mm diameter single crystal CZ silicon ingots (designated asuniform samples 1, 2 and 3) were each prepared at a pull rate of 0.9 mmper minute, at a temperature gradient of from about 35° K per cm toabout 46° K per cm, and at an ingot nitrogen concentration of from about1*10¹⁴ atoms per cubic centimeter to about 1*10¹⁵ atoms per cubiccentimeter. Comparative 300 mm diameter single crystal CZ silicon ingots(designated as non-uniform samples 1 and 2) were each prepared at a pullrate of 0.78 mm per minute, at a temperature gradient of about 51° K percm, and at an ingot nitrogen concentration of from about 3*10¹³ atomsper cubic centimeter to about 2*10¹⁴ atoms per cubic centimeter. Waferswere sliced from the ingots and were subjected to an oxygenprecipitation heat treatment by annealing the wafer for 3 hours at 780°C. and then 16 hours at 1000° C.

As depicted in FIG. 1 the average BMD size (diameter) increase from thecenter of the wafer to the edge of the wafer was about 47% and about 37%for non-uniform prior art samples 1 and 2, respectively. The averagedBMD size increase from 10 mm to the edge and the edge of the wafer wasabout 28% and about 29% within the 10 mm radius for non-uniform priorart samples 1 and 2, respectively. As depicted in FIG. 2, the averageBMD density increase from the center of the wafer to the edge of thewafer was about 660% and about 285% for non-uniform prior art samples 1and 2, respectively. The averaged BMD density increase from 10 mm to theedge of the wafer and the edge of the wafer was about 357% and about308% within the 10 mm radius for non-uniform prior art samples 1 and 2,respectively. The edge band was characterized by a band ofprecipitations with relatively higher density and relatively large size.

As depicted in FIG. 21 the average BMD size decrease from the center ofthe wafer to the edge of the wafer was about 6%, 7% and 4% for uniformsamples 1, 2 and 3 of the present disclosure, respectively. The averageBMD size decrease from the center of the wafer to the edge of the waferwas about 6%, 3% and 1% for uniform samples 1, 2 and 3 of the presentdisclosure, respectively. As depicted in FIG. 22, the average BMDdensity decrease from the center of the wafer to the edge of the waferwas about 23%, 37% and 4% for uniform samples 1, 2 and 3 of the presentdisclosure, respectively. As depicted in FIG. 22, the average BMDdensity decrease from the center of the wafer to the edge of the waferwas about 6%, 12% and 16% for uniform samples 1, 2 and 3 of the presentdisclosure, respectively. There was no detectable edge band in theseuniform samples because of the decreases in both density and size.

The results of the experiment demonstrate that through simulations ofseveral combinations, that the radii of oxygen precipitates in the edgeregion of a conventional process can be reduced significantly withoutany significant change void size. If annealing is done at 1100° C. thenaverage BMD densities can also be reduced, while still keeping thedensity above 1*10⁸ per cm³, which has been shown in prior art to besufficient for gettering.

This written description uses examples to disclose the invention,including the best mode, and also to enable any person skilled in theart to practice the invention, including making and using any devices orsystems and performing any incorporated methods. The patentable scope ofthe invention is defined by the claims, and may include other examplesthat occur to those skilled in the art. Such other examples are intendedto be within the scope of the claims if they have structural elementsthat do not differ from the literal language of the claims, or if theyinclude equivalent structural elements with insubstantial differencesfrom the literal languages of the claims.

When introducing elements of the present invention or the embodiment(s)thereof, the articles “a”, “an”, “the” and “said” are intended to meanthat there are one or more of the elements. The terms “comprising”,“including” and “having” are intended to be inclusive and mean thatthere may be additional elements other than the listed elements.

1-24. (canceled)
 25. A method of controlling an edge band of oxygenprecipitates in wafers sliced from a nitrogen-doped CZ silicon crystalingot and thermally treated at 780° C. for 3 hours and then at 1000° C.for 16 hours wherein the method is implemented by a computing deviceincluding a processor coupled to a memory, the method comprising:determining, by the computing device, by simulation, a combination of(i) nitrogen-doped CZ silicon crystal diameter, (ii) nitrogen-doped CZsilicon crystal ingot pull rate or nitrogen-doped CZ silicon crystalingot pull rate range, (iii) nitrogen-doped CZ silicon crystal ingotnitrogen concentration or nitrogen-doped CZ silicon crystal ingotnitrogen concentration range, and (iv) nitrogen-doped CZ silicon crystalingot surface temperature gradient or nitrogen-doped CZ silicon crystalingot surface temperature range that enables the preparation of anitrogen-doped CZ silicon crystal ingot from molten silicon by the CZprocess wherein a thermally treated wafer sliced therefrom having anedge band in a region extending from about 1000 μm to the edge of saidwafer and to the edge of said wafer and is characterized by oxygenprecipitates having an average diameter of from about 30 nm to about 100nm, wherein (i) the nitrogen-doped CZ silicon crystal ingot has adiameter of from about 150 mm to about 450 mm and (ii) the nitrogenconcentration in the nitrogen-doped CZ silicon crystal ingot is fromabout 1*10¹³ atoms per cm³ to about 1*10¹⁵ atoms per cm³, wherein thesimulation comprises at least one iteration of a simulation schemecomprising: (1) receiving, by the computing device, values for at least(i) a nitrogen-doped CZ silicon crystal ingot diameter, (ii) anitrogen-doped CZ silicon crystal ingot pull rate or a nitrogen-doped CZsilicon crystal ingot pull rate range, (iii) a nitrogen-doped CZ siliconcrystal ingot nitrogen concentration or a nitrogen-doped CZ siliconcrystal ingot nitrogen concentration range and (iv) a nitrogen-doped CZsilicon crystal ingot surface temperature gradient or a nitrogen-dopedCZ silicon crystal surface ingot temperature gradient range, andsimulating, by the computing device, a thermally treated wafer radialbulk micro defect size distribution in a region extending from thecenter of said wafer to the edge of said wafer based on the receivedvalues; (2) receiving, by the computing device, values for at least (i)the nitrogen-doped CZ silicon crystal ingot diameter, (ii) thenitrogen-doped CZ silicon crystal ingot pull rate or the nitrogen-dopedCZ silicon crystal ingot pull rate range and (iii) the nitrogen-doped CZsilicon crystal ingot nitrogen concentration or the nitrogen-doped CZsilicon crystal ingot nitrogen concentration range, and simulating, bythe computing device, a thermally treated wafer radial bulk micro defectdensity distribution in a region extending from the center of said waferto the edge of said wafer based on the received values; (3) receiving,by the computing device, values for at least (i) the nitrogen-doped CZsilicon crystal ingot diameter, (ii) the nitrogen-doped CZ siliconcrystal ingot pull rate or the nitrogen-doped CZ silicon crystal ingotpull rate range, (iii) the nitrogen-doped CZ silicon crystal ingotnitrogen concentration or the nitrogen-doped CZ silicon crystal ingotnitrogen concentration range and (iv) the nitrogen-doped CZ siliconcrystal ingot surface temperature gradient or the nitrogen-doped CZsilicon crystal ingot surface temperature gradient range and simulating,by the computing device, a thermally treated wafer oxygen precipitationdensity distribution in a region extending from the center of said waferto the edge of said wafer; and (4) simulating, by the computing device,the average size of the thermally treated wafer edge band oxygenprecipitates based on the simulated values for (i) the thermally treatedwafer radial bulk micro defect size distribution from the center of saidwafer to the edge of said wafer, (ii) the thermally treated wafer radialbulk micro defect density distribution from the center of said wafer tothe edge of said wafer, and (iii) the thermally treated wafer oxygenprecipitation density distribution in a region extending from the centerof said wafer to the edge of said wafer, wherein the computing devicepredicts the thermally treated wafer edge band by simulation to compriseoxygen precipitates having an average diameter of from about 30 nm toabout 100 nm, and pulling the nitrogen-doped CZ silicon crystal ingotfrom the molten silicon at the simulated values of nitrogen-doped CZsilicon crystal ingot pull rate or nitrogen-doped CZ silicon crystalingot pull rate range, nitrogen-doped CZ silicon crystal ingot nitrogenconcentration or nitrogen-doped CZ silicon crystal ingot nitrogenconcentration range, and nitrogen-doped CZ silicon crystal ingot surfacetemperature gradient or nitrogen-doped CZ silicon crystal ingot surfacetemperature range to produce the nitrogen-doped CZ silicon crystal ingotfrom which the treated wafers are produced.
 26. The method of claim 25wherein the pull rate is from about 0.4 mm per minute to about 1.5 mmper minute and the temperature gradient is from about 10° K per cm toabout 50° K per cm at an average crystal surface temperature of fromabout 1300° C. to about 1415° C.
 27. The method of claim 25 wherein thethermally treated wafer has an oxygen precipitation density of fromabout 1*10⁸ atoms per cm³ to about 1*10¹⁰ atoms per cm³
 28. The methodof claim 25 wherein the treated wafer (i) has a radial bulk micro defectsize distribution characterized by an increase in bulk micro defect sizein a region extending from the center of said wafer to the edge of saidwafer of less than 20% and (ii) has an increase in radial bulk microdefect density from the center of said wafer to the edge of said waferof less than 200%.
 29. The method of claim 25 wherein the thermallytreated wafer is characterized by an increase in radial bulk microdefect size in a region extending from about 10 mm to the edge of saidwafer to the edge of said wafer of less than 15%.
 30. The method ofclaim 25 wherein the thermally treated wafer is characterized by anincrease in radial bulk micro defect density in a region extending fromabout 10 mm to the edge of said wafer to the edge of said wafer of lessthan 100%.
 31. The method of claim 25 further comprising receiving anitrogen-doped CZ silicon crystal ingot annealing temperature, saidannealing temperature being from about 1000° C. to about 1100° C., and(1) simulating the thermally treated wafer radial bulk micro defect sizedistribution in a region extending from the center of said wafer to theedge of said wafer on the basis of the combination of (i) thenitrogen-doped CZ silicon crystal ingot diameter, (ii) thenitrogen-doped CZ silicon crystal ingot pull rate or the nitrogen-dopedCZ silicon crystal pull rate range, (iii) the nitrogen-doped CZ siliconcrystal nitrogen concentration or the nitrogen-doped CZ silicon crystalingot nitrogen concentration range, (iv) the nitrogen-doped CZ siliconcrystal ingot surface temperature gradient or the nitrogen-doped CZsilicon crystal ingot surface temperature gradient range, and thenitrogen-doped CZ silicon crystal ingot annealing temperature, and (2)simulating the thermally treated wafer radial bulk micro defect densitydistribution in a region extending from the center of said wafer to theedge of said wafer on the basis of the combination of (i) thenitrogen-doped CZ silicon crystal ingot diameter, (ii) thenitrogen-doped CZ silicon crystal ingot pull rate or the nitrogen-dopedCZ silicon crystal pull rate range, (iii) the nitrogen-doped CZ siliconcrystal ingot nitrogen concentration or the nitrogen-doped CZ siliconcrystal ingot nitrogen concentration range, and (iv) the nitrogen-dopedCZ silicon crystal ingot annealing temperature.
 32. The method of claim25 wherein the wafer is a polished and epitaxial wafer made by slicing anitrogen-doped CZ silicon crystal ingot, the wafer comprising a frontsurface, a back surface, a central plane between the front and backsurfaces, a circumferential edge joining the front and back surface, acentral axis perpendicular to the central plane, a bulk layer whichcomprises the region of the wafer between the central plane and frontsurface.
 33. The method of claim 25 wherein the pull rate is from about0.7 mm per minute to about 1.0 mm per minute and the temperaturegradient is from about 30° K per cm to about 50° K per cm at an averagecrystal surface temperature of from about 1300° C. to about 1415° C. 34.The method of claim 25 wherein the pull rate is from about 0.8 mm perminute to about 1.0 mm per minute and the temperature gradient is fromabout 25° K per cm to about 50° K per cm an average crystal surfacetemperature of from about 1300° C. to about 1415° C.
 35. The method ofclaim 25 wherein the nitrogen-doped CZ silicon crystal ingot or waferhas a diameter of about 300 mm, the pull rate is from about 0.85 toabout 1.5 mm/min and the temperature gradient is from about 10° K per cmto about 35° K per cm at an average crystal surface temperature of fromabout 1300° C. to about 1415° C.
 36. The method of claim 25 wherein thethermally treated wafer is a post epitaxial thermally treated wafer.